hp-Adaptive Finite Elements for Maxwell’s Equations

This is a progress report on our current work on hp-adaptive finite elements for Maxwell’s equations. I recall the main definitions [2], and show how the recent progress on the ftp interpolation error estimates [3] has led to a fully automatic ftp adaptivity based on the idea of minimizing the ftp-interpolation error for a reference solution corresponding to a globally ftp-refined grid [5]. Critical to the implementation of these ideas is a our new data structure for ftp discretizations [4], supporting anisotropic refinements, and the calculation of prolongation operator for multigrid operations.